Recursive Estimation of Autoregressions

Abstract

SUMMARY This paper is concerned with the recursive estimation of autoregressive models, in particular the realtime determination of the order of such a specification. A model selection criterion based on the minimum description length principle due to Rissanen is discussed and strong consistency in the stationary situation is shown. Alternative criteria are also considered and modifications required to introduce forgetting when the procedures are implemented in the non-stationary case are presented. Some simulation evidence on the performance of the criteria when applied to stationary and non-stationary processes is given.